Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the slope of a line represent in a real-world context?

Back

The slope represents the rate of change between two variables. For example, in a distance-time graph, the slope indicates speed.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation f(x) = mx + b.

Front

If f(x) = -5x + 10, what is f(2)?

Back

f(2) = -5(2) + 10 = 0.

Front

What is the correlation coefficient and what does it indicate?

Back

The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1.

Front

What does a correlation coefficient of r = -0.95 indicate?

Back

It indicates a strong negative correlation, meaning as one variable increases, the other variable tends to decrease.

Front

How do you convert the equation -6x - 2y = 9 to slope-intercept form?

Back

To convert to slope-intercept form (y = mx + b), solve for y: -2y = 6x + 9, then y = -3x - 4.

Front

What is the slope of the line represented by the equation y = -3x - 4?

Back

The slope is -3.

Front

If a car uses 2 gallons of gas every hour, what is the slope of the line representing gas usage over time?

Back

The slope is 2, representing the rate of gas consumption per hour.